Mathematics 9709 · AS & A Level · Probability

Probability — practice question

Georgie owns a red scarf, a blue scarf and a yellow scarf. On each day, she chooses to wear exactly one of these scarves. The probabilities of selecting the three colours are $0.2$, $0.45$ and $0.35$ respectively. If she wears a red scarf, she always also wears a hat. If she wears a blue scarf, the probability that she wears a hat is $0.4$. If she wears a yellow scarf, the probability that she wears a hat is $0.3$.
(a)[2]

Find the probability that Georgie wears a hat on a randomly selected day.

(b)[3]

Find the probability that Georgie wears a yellow scarf on a randomly selected day, given that she does not wear a hat.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: A correct probability expression, for example $0.2+0.45\times0.4+0.35\times0.3$

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